If the electric potential on the surface of inner most sphere is zero , then the relation between `r_(1) , r_(2)` and `r_(3)` is (here `sigma` is surface charge density )

Options

A. `r_(3) = r_(1) + r_(2)`
B. `r_(2) = sqrt(r_(1) r_(3))`
C. `r_(2) = r_(1) + r_(3)`
D. `r_(2) = r_(3) - r_(1)`

Answer

C

Explanation

At inner surface
`V = (sigma r_(1))/(epsi_(0)) + ((-sigma) r_(2))/(epsi_(0)) + (sigmar_(3))/(epsi_(0)) = 0 `
`(sigma)/(epsi_(0))[r_(1) - r_(2) + r_(3)] = 0`
`therefore r_(2) = r_(1) + r_(3)`